This invention relates, in general, to feedback control systems and, more specifically, to predictive control of dynamic systems.
Systems requiring the control of their outputs are varied and numerous. For example, robot position, missile paths, regulator outputs, and elevator travel are all candidates for control systems which specify a desired output position, speed, voltage, etc., and want the system output to match the specified output as closely as possible. In order to achieve these results, many of the systems employ the classical form of feedback from the output to the input of the system being controlled. With such classical feedback, a comparison is made between the desired and actual output of the system and any error is amplified and applied to the input of the system to correct the error. Such types of systems are in widespread use according to the prior art. However, when very precise output control is desired and/or the dynamic characteristics of the system are subject to rapid fluctuation, the degree of reliability and success with conventional classical feedback systems is limited.
In order to make the output of the controlled system more closely match the desired output, a method of predictive control is used in conjunction with classical feedback systems. According to predictive control, a mathematical model of the controlled system which represents the dynamic characteristics of the controlled system, is used to predict the output, in advance, of the controlled system. This is done by applying input values to the model and noting the difference between the output of the model and the desired output of the controlled system. Any difference is considered an error signal and is used to adjust the input to the controlled system so that it will give the proper output. In some predictive control systems, the model of the controlled system may be changed during the operation of the system to compensate for changes in the dynamic characteristics of the system.
Further description of a predictive control system using mathematical models is contained in "Predictive Control Using Impulse Response Models" by P. M. Bruijn, et al., Proceedings of IFAC/IFIP Conference on Digital Computer Applications to Process Control, Dusseldorf, Federal Republic of Germany, October, 1980.
To obtain the inputs which must be applied to a controlled system to give the best output signal, calculations are made based upon what is known about the controlled system for a period of time into the future, known as the "prediction horizon" (PH). Normally, a prediction horizon usually encompasses 3 to 10 discrete time computation or sampling intervals beyond the present time for which the input to the controlled system is being determined.
As a general rule, the more frequently a determination can be made about the value of an input signal to the controlled system, the smoother the input signal will be and the less likely the output signal or output of the controlled system will exhibit any unstable characteristics. For this reason, it is desirable to make the computations concerning the inputs to the controlled system as quickly and efficiently as possible. Such calculations determine the data rate at which predictive control must be implemented. Higher data rates result in less inter-sample ripple on the system output, and allow predictive control to improve trajectory or output following for a wider range of systems. Therefore, it is desirable, and it is an object of this invention, to provide a predictive control system which calculates the future input sequences to the controlled system as rapidly as possible.
The method of calculation of the input sequences also effects the stability of the controlled system. For example, some prior art systems use calculating methods which can cause output instabilities in certain types of controlled systems, such as non-minimum phase systems. Therefore, it is also desirable, and it is another object of this invention, to provide a predictive control system which exhibits stable characteristics with all types of controlled systems, including non-minimum phase systems.